The diagonal lemma (which can be used to prove the Gödel-Tarski Theorem, among others) apparently goes, in a nutshell, suppose you have a one-place formula A(.) with domain the set of codes of sentences. I use quotation marks in this way : "M" is the code of M. Define the 2-place relation sub: If x ="f(.)", then sub(x,x) = "f(x)" Define B(x) as A(sub (x,x)) Define S as B("B(x)") retracing, S is true iff A("S") is. Nice. What I do not understand is that the proof notes that S and A("S") are equivalent but not the same. It appears to me from the construction that they are the same. What am I missing? Thanks.